randRangeNonZero(-5, 5)
randRangeNonZero(-5, 5)
randRange(0, 1)
["x", "y"][COMPONENT]
$._("horizontally")
$._("vertically")
[HORIZONTAL, VERTICAL][COMPONENT]
COMPONENT ? randRange(-5, 5) : AX
COMPONENT ? AY : randRange(-5, 5)
COMPONENT ? randRange(-5, 5) : -AX
COMPONENT ? -AY : randRange(-5, 5)
COMPONENT ? randRangeNonZero(-5, 5) : randRangeExclude(-5, 5, [AX])
COMPONENT ? randRangeExclude(-5, 5, [AY]) : randRangeNonZero(-5, 5)
randRangeNonZero(max(-9, -9 - AX), min(9, 9 - AX))
randRangeNonZero(max(-9, -9 - AY), min(9, 9 - AY))
randRangeNonZero(max(-9, -9 - BX), min(9, 9 - BX))
randRangeNonZero(max(-9, -9 - BY), min(9, 9 - BY))
randRangeNonZero(max(-9, -9 - CX), min(9, 9 - CX))
randRangeNonZero(max(-9, -9 - CY), min(9, 9 - CY))
randRangeNonZero(max(-9, -9 - DX), min(9, 9 - DX))
randRangeNonZero(max(-9, -9 - DY), min(9, 9 - DY))
COMPONENT ? randRange(-9, -9) : AOX
COMPONENT ? AOY : randRange(-9, -9)
COMPONENT ? randRangeNonZero(-5, 5) : randRangeExclude(-5, 5, [AX])
COMPONENT ? randRangeExclude(-5, 5, [AY]) : randRangeNonZero(-5, 5)
[BX, BY, BOX, BOY]
shuffle([ANS, [CX, CY, COX, COY], [DX, DY, DOX, DOY], [EX, EY, EOX, EOY]])
$.inArray(ANS, SHUF)
[
["b", "pink"],
["c", "green"],
["d", "purple"],
["e", "red"]
][INDEX]
SHUF[0]
SHUF[1]
SHUF[2]
SHUF[3]
1 + 0.8 / sqrt(AX * AX + AY * AY)
1 + 0.8 / sqrt(BX * BX + BY * BY)
1 + 0.8 / sqrt(CX * CX + CY * CY)
1 + 0.8 / sqrt(DX * DX + DY * DY)
1 + 0.8 / sqrt(EX * EX + EY * EY)
Which vector has the same COMPONENT_NAME component as \vec a?
graphInit({
range: 10,
scale: 20,
tickStep: 1,
axisArrows: "<->",
axisLabels: ['x', 'y']
});
style({
stroke: BLUE,
color: BLUE
}, function() {
line( [AOX, AOY], [AOX + AX, AOY + AY], { arrows: "->" } );
label( [AOX + AF * AX, AOY + AF * AY], "\\vec a" );
});
style({
stroke: PINK,
color: PINK
}, function() {
line( [BOX, BOY], [BOX + BX, BOY + BY], { arrows: "->" } );
label( [BOX + BF * BX, BOY + BF * BY], "\\vec b" );
});
style({
stroke: GREEN,
color: GREEN
}, function() {
line( [COX, COY], [COX + CX, COY + CY], { arrows: "->" } );
label( [COX + CF * CX, COY + CF * CY], "\\vec c" );
});
style({
stroke: PURPLE,
color: PURPLE
}, function() {
line( [DOX, DOY], [DOX + DX, DOY + DY], { arrows: "->" } );
label( [DOX + DF * DX, DOY + DF * DY], "\\vec d" );
});
style({
stroke: RED,
color: RED
}, function() {
line( [EOX, EOY], [EOX + EX, EOY + EY], { arrows: "->" } );
label( [EOX + EF * EX, EOY + EF * EY], "\\vec e" );
});
\large\ANSC{\vec ANSL}
\large\pink{\vec b}\large\green{\vec c}\large\purple{\vec d}\large\red{\vec e}
The COMPONENT_NAME component of a vector is the amount it moves DIRECTION.
style({ stroke: BLACK });
line([AOX + AX, AOY], [AOX + AX, AOY + AY], { arrows: "->" });
style({ strokeDasharray: "."});
line([AOX, AOY], [AOX + AX, AOY]);
style({ stroke: BLACK });
line([AOX, AOY + AY], [AOX + AX, AOY + AY], { arrows: "->" });
style({ strokeDasharray: "."});
line([AOX, AOY], [AOX, AOY + AY]);
Vector \vec a starts at COMPONENT_NAME = [AOX, AOY][COMPONENT] and ends at COMPONENT_NAME = [AOX + AX, AOY + AY][COMPONENT].
Therefore, vector \vec a moves DIRECTION [AX, AY][COMPONENT] units.
Therefore, vector \vec a moves DIRECTION 1 unit.
style({ stroke: BLACK, strokeDasharray: "" });
line([ANS[2] + ANS[0], ANS[3]], [ANS[2] + ANS[0], ANS[3] + ANS[1]], { arrows: "->" });
style({ strokeDasharray: "."});
line([ANS[2], ANS[3]], [ANS[2] + ANS[0], ANS[3]]);
style({ stroke: BLACK, strokeDasharray: "" });
line([ANS[2], ANS[3] + ANS[1]], [ANS[2] + ANS[0], ANS[3] + ANS[1]], { arrows: "->" });
style({ strokeDasharray: "."});
line([ANS[2], ANS[3]], [ANS[2], ANS[3] + ANS[1]]);
The only other vector that moves DIRECTION [AX, AY][COMPONENT] units is
\vec ANSL.
The only other vector that moves DIRECTION 1 unit is \vec ANSL.
randRangeNonZero(-8, 8)
randRangeNonZero(-8, 8)
randRangeNonZero(max(-9, -9 - AX), min(9, 9 - AX))
randRangeNonZero(max(-9, -9 - AY), min(9, 9 - AY))
1 + 0.8 / sqrt(AX * AX + AY * AY)
randRange(0, 1)
["x", "y"][COMPONENT]
$._("horizontally")
$._("vertically")
[HORIZONTAL, VERTICAL][COMPONENT]
[AX, AY][COMPONENT]
What is the value of the COMPONENT_NAME component of \vec a?
graphInit({
range: 10,
scale: 20,
tickStep: 1,
labels: true,
axisArrows: "<->",
axisLabels: ['x', 'y']
});
style({
stroke: BLUE,
color: BLUE
}, function() {
line([AOX, AOY], [AOX + AX, AOY + AY], { arrows: "->" });
label([AOX + AF * AX, AOY + AF * AY], "\\vec a");
});
ANS
The COMPONENT_NAME component of a vector is the amount it moves DIRECTION.
style({ stroke: BLACK });
line([AOX + AX, AOY], [AOX + AX, AOY + AY], { arrows: "->" });
style({ strokeDasharray: "."});
line([AOX, AOY], [AOX + AX, AOY]);
style({ stroke: BLACK });
line([AOX, AOY + AY], [AOX + AX, AOY + AY], { arrows: "->" });
style({ strokeDasharray: "."});
line([AOX, AOY], [AOX, AOY + AY]);
Vector \vec a starts at COMPONENT_NAME = [AOX, AOY][COMPONENT] and ends at COMPONENT_NAME = [AOX + AX, AOY + AY][COMPONENT].
Therefore, the COMPONENT_NAME component of \vec a is ANS